Is stalemate worth half a point?

Yes. Stalemate is an ordinary draw, so both players score half a point, exactly as they would after a threefold repetition or a handshake. There is no partial credit for having more material. A player a queen and two rooks up who stalemates his opponent scores the same half point as the man he was beating.

Do you have to claim a stalemate?

No. The game ends the moment the stalemate position appears on the board, whether either player notices or not. It is not a claim like threefold repetition or the fifty-move rule. If moves are played on afterwards, the arbiter winds the game back to the stalemate and the result is a draw.

Was stalemate always a draw?

No. English rules of the eighteenth century gave the win to the player who had been stalemated, which is the reverse of a loss. Other traditions counted it as a win for the side delivering it, or as a half win. The draw is what international play settled on in the nineteenth century, once players from different countries needed one rulebook.

Why is stalemate a draw?

White is a pawn up, it is his move, and he has just drawn the game. King on a8, pawn on a7, black king on c7. Count his legal moves: b7 and b8 belong to the black king, a7 is occupied by his own pawn, and that pawn cannot walk through its own king. Nothing. And no check.

White to move and stalemate. He is a pawn up, he is not in check, and he has no legal move on the board. Half a point each.

Having no move is not the same as being beaten

Chess is won by attacking the king so that the attack cannot be answered, and every word of that matters. The king has to be under attack. A stalemated king is not attacked by anything: he is untouched, unthreatened, and simply out of moves, and no rule in the game says that running out of moves is losing. You cannot pass your turn either, so the position needs a ruling of its own, and Article 5.2 of the FIDE Laws gives it one. Draw.

Turn it round and see what you would be signing up for. If stalemate were a win, then boxing an opponent in would beat him just as well as mating him, and checkmate would stop being the object of the game. Half the defensive resources in chess would vanish with it.

It has not always been a draw

The rule is a settlement, not a law of nature. English players in the eighteenth century scored stalemate as a win for the player who had been stalemated, which is the exact opposite of a loss and must have made for some strange endgames. Elsewhere it was scored the other way, or as a half win. The modern draw is what the international game agreed on during the nineteenth century, when players from different countries began meeting over the board and somebody had to choose.

Endgame theory sits on top of it

Move that first diagram one file across and it turns into a win.

King on b8, pawn on b7, black king on d7. Now the white king has a7 to step to: 1.Ka7 Kc7 2.b8=Q+ and the new queen is defended by her king.

One file, and it is the difference between half a point and a whole one. A rook’s pawn is the only pawn whose king has no square on the far side to step aside to, so a bare king that reaches a8 in front of an a-pawn draws, and the same defence against a b-pawn loses. Every king and pawn ending you will ever study starts from facts of that shape, and they exist only because stalemate is a draw.

Which also makes stalemate a weapon rather than an accident. Down a rook with nothing left, the plan is often not to survive but to run out of moves at a moment of your choosing. From the winning side of the board the same fact is a hazard, and there is a page on how to avoid stalemate. For the milder version, where you do have a legal move and every one of them ruins you, see zugzwang.